Chúng minh rằng:

(2a+2b-c)^2+(2b+2c-a)^2+(2c+2a-b)^2=9(a^2+b^2+c^2)

`(2a+2b-c)^2+(2b+2c-a)^2+(2c+2a-b)^2`

`=4a^2+8ab-4ac+4b^2-4bc+c^2+(2b+2c-a)^2+(2c+2a-b)^2`

`=4a^2+8ab-4ac+4b^2-4bc+c^2+4b^2+8bc-4ab+4c^2+a^2-4ac+4c^2+4a^2+8ac-4bc-4ab+b^2`

`=4a^2+a^2+4a^2+8ab-4ab-4ab-4ac-4ac+8ac+4b^2+4b^2+b^2-4bc+8bc-4bc+c^2+4c^2+4c^2`

`=9a^2+8ab-4ab-4ab-4ac-4ac+8ac+4b^2+4b^2+b^2-4bc+8bc-4bc+c^2+4c^2+4c^2`

`=9a^2-4ac-4ac+8ac+4b^2+4b^2+b^2-4bc+8bc-4bc+c^2+4c^2+4c^2`

`=9a^2+4b^2+4b^2+b^2-4bc+8bc-4bc+c^2+4c^2+4c^2`

`=9a^2+9b^2-4bc+8bc-4bc+c^2+4c^2+4c^2`

`=9a^2+9b^2+c^2+4c^2+4c^2`

`=9a^2+9b^2+9c^2`
`=9(a^2+b^2+c^2)`

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